Holographic data storage systems store information or data based on the concept of a signal beam interfering with a reference beam at a holographic storage medium. The interference of the signal beam and the reference beam creates a holographic representation, i.e., a hologram, of data elements as a pattern of varying refractive index and/or absorption imprinted in a volume of a storage or recording medium such as a photopolymer or photorefractive crystal. Combining a data-encoded signal beam, referred to as an object beam, with a reference beam creates the interference pattern at the storage medium. A spatial light modulator (SLM), for example, can create the data-encoded signal beam. The interference pattern induces material alterations in the storage medium that generate the hologram. The formation of the hologram in the storage medium is a function of the relative amplitudes and polarization states of, and phase differences between, the signal beam and the reference beam. The hologram is also dependent on the wavelengths and angles at which the signal beam and the reference beam are projected into the storage medium. After a hologram is created in the storage medium, projecting the reference beam into the storage medium reconstructs the original data-encoded signal beam. The reconstructed signal beam may be detected by using a detector, such as CMOS photo-detector array or the like. The detected data may then be decoded into the original encoded data.
In a page-oriented holographic data storage device, it is advantageous to minimize the size of the holograms in order to achieve maximum storage density. One method of accomplishing this is minimizing the size of the page imaging aperture. However, minimizing the size of the aperture has the consequence of increasing blur, in terms of broadening the pixel spread function (PSF) in the page images. This blur decreases the signal-to-noise ratio (SNR) of the holographic storage device, which increases the bit error rate (BER) of the system, and which in turn limits the storage density.
Since blur in an image is a deterministic process, much of the SNR loss may be reclaimed by digitally post-processing the detected page image. Traditionally, the detected image is convolved with a small kernel matrix w, also known as a kernel, representing an inverse blurring operation (de-convolution), thereby implementing a finite impulse response (FIR) filter equalization.
The kernel of a FIR filter, for example a 3×3 or a 5×5 matrix, may be determined by several methods known in the current art. For example, if the page image pixel spread function is known, a zero-forcing equalizer may be designed by calculating the linear inverse of the PSF. An example of the zero-forcing method is described in “Channel estimation and intra-page equalization for digital volume holographic data storage,” by V. Vadde and B. Kumar in Optical Data Storage 1997, pp. 250-255, 1997. Another approach is to choose FIR filter coefficients that minimize the difference between the equalized data page image and the original data page. Such a method is described in “Application of linear minimum mean-squared-error equalization for volume holographic data storage,” by M. Keskinoz and B. Kumar in Applied Optics, vol. 38, no. 20, Jul. 10, 1999.
In a page-oriented holographic data storage device, optical detector arrays are employed to read holographic reconstructed data images. The detector array is typically pixel-matched to the holographic image. An example of a pixel-matched data storage is described by R. Shelby et al. in “Pixel-matched holographic data storage with megabit pages,” Opt. Letter 22, pp. 1509-1511, 1997, which is incorporated herein in its entirety by reference. This approach requires exceedingly high performance optics and mechanics in order to achieve the precise alignment of each data pixel image to a detector pixel of the same size. Commercial systems have been designed using detector arrays that spatially sample the image at or above the Nyquist rate in order to read misaligned or distorted images. Such a system is described by S. Redfield et al. in “Tamarack Optical Head Holographic Storage,” Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. Sincerbox, eds., (Springer-Verlag, New York, 2000), which is incorporated herein in its entirety by reference.
However, there are a number of factors that affect the performance of the detector array. For example, there are a number of factors create variations in the width or shape of the pixel spread function throughout the field of view. For example, variations may be caused by lens aberrations and misalignment; by distortions, shrinkage, and other non-ideal media responses; and by misalignment and wavefront errors in the reconstructing reference beam. A significant consequence of these effects in a pixel-matched system is the degradation of the pixel matching, because image distortion shifts local areas of the image with respect to the detector pixels. For example, a uniform shrinkage of the medium causes the holographic image to be magnified, producing a radial displacement such that data pixel images are no longer centered on their respective detector pixels. Even neglecting distortions, image shifts and rotations caused by medium misregistration and other non-ideal component alignments dictate that micro-actuators are employed in order to effect dynamic image-to-detector alignment.
G. Burr et al. in “Compensation for pixel misregistration in volume holographic data storage,” Opt. Letter 26, pp. 542-544, 2001 and P. Yoon et al. in “Image Compensation for Sub-pixel Misalignment in Holographic Data Storage,” ISOM Proceedings, 2004, have proposed methods for restoring the fidelity of partially misaligned (less than half a pixel) images, but realistic tolerance models indicate that image shifts of up to several hundreds of microns may be encountered in a unit in the field.
Sampling theory indicates that if the holographic image is spatially sampled in each linear dimension at least twice the frequency of its highest component (the Nyquist frequency), then the signal may be captured losslessly. For holographic data storage (especially in the Fourier Transform geometry), it is advantageous to limit the spatial bandwidth of the data beam to only slightly higher than the Nyquist frequency of the data pattern. Since the data pattern can contain at most one cycle per two pixels, the Nyquist frequency becomes one sample per pixel. Typically, an aperture in a Fourier plane is used to band-limit the data beam, thereby minimizing the size of the holograms.
Although the spectral content of the electromagnetic field impinging on the detector may be captured with one synchronous sample per pixel in theory, the detector can only detect irradiance but not field strength in practice. The spectrum of an irradiance pattern is the autocorrelation of the spectrum of the corresponding electromagnetic field distribution; therefore the spatial bandwidth of the signal actually available to the system doubles. Thus it requires at least two detector samples per data pixel image (for a total of four detector pixels per data image pixel in two dimensions) in order to losslessly sample the irradiance pattern at the detector. This approach is described by T. Visel et al. in “Distortion correction of a reconstructed holographic data image,” U.S. Pat. No. 5,511,058, and by A. Hartmann in “Method and apparatus for processing of reconstructed holographic images of digital data patterns,” U.S. Pat. No. 5,694,448, both of which are incorporated herein in their entirety by reference. However, the irradiance pattern is not of primary importance to the operation of the device. It is instead the underlying data pattern that is significant. The magnitude-squared transformation that generates the higher harmonics creates new problems because it is non-linear.
Another solution is to make the ratio of detector pixels to data image pixels closer to one than to four. This method is described by G. Burr in “Holographic data storage with arbitrarily misaligned data pages,” Opt. Letter 27, pp. 542-544, 2002, which is incorporated herein it its entirety by reference. However, this method requires an aperture much larger than Nyquist, which degrades quickly with distortions and noise.
Therefore, new methods and systems for addressing the above issues of the prior art methods are needed. In particular, methods for recovering arbitrarily aligned and distorted data pages are needed to improve the storage density of the holographic data storage system.